Best Known (17, 17+19, s)-Nets in Base 64
(17, 17+19, 257)-Net over F64 — Constructive and digital
Digital (17, 36, 257)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (7, 26, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (1, 10, 80)-net over F64, using
(17, 17+19, 337)-Net in Base 64 — Constructive
(17, 36, 337)-net in base 64, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- (7, 26, 257)-net in base 64, using
- 2 times m-reduction [i] based on (7, 28, 257)-net in base 64, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- 2 times m-reduction [i] based on (7, 28, 257)-net in base 64, using
- digital (1, 10, 80)-net over F64, using
(17, 17+19, 589)-Net over F64 — Digital
Digital (17, 36, 589)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6436, 589, F64, 19) (dual of [589, 553, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(6436, 819, F64, 19) (dual of [819, 783, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 819 | 642−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(6436, 819, F64, 19) (dual of [819, 783, 20]-code), using
(17, 17+19, 695731)-Net in Base 64 — Upper bound on s
There is no (17, 36, 695732)-net in base 64, because
- 1 times m-reduction [i] would yield (17, 35, 695732)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 1645 519368 427483 255773 576799 749560 904829 687507 077075 436769 996338 > 6435 [i]